play whole islands, make home the path itself, draw tutor diagrams, add tedi

- Home is now the island path of every unit with one clear Start button on the
  current island; the six-card dashboard is gone.
- Start opens /nodes/{id}/quiz (4 questions) instead of one-question lessons, so
  an island takes one round instead of ~11. Lessons stay one tap away in the sheet.
- Tutor answers render the backend's validated diagram (plane, number line,
  fraction) as React SVG; function expressions go through a small parser, no eval.
- Tedi, the mobile-preview mascot, joins as the fourth companion with all six moods
  and an onboarding slide.
- Light polish: 3D buttons, header gradients, warmer page background.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/nav/routes.ts

@@ -7,7 +7,8 @@ export type Route =
   | { name: 'profile' }
   | { name: 'unit'; unitId: string }
   | { name: 'lesson'; lessonId: number; nodeId?: string }
-  | { name: 'quiz'; lessonId: number; nodeId?: string }
+  /** بدونِ lessonId یعنی آزمونِ کلِ جزیره (nodeId لازم است). */
+  | { name: 'quiz'; lessonId?: number; nodeId?: string }
   | { name: 'notifications' }
   | { name: 'leaderboard' }
   | { name: 'characters' }